Examples for the Infinite Dimensional Morse Lemma *

Abstract

Examples are presented which show how to use the Morse lemma in specific infinite dimensional examples and what can go wrong if various hypotheses are dropped. One of the examples shows that the version of the Morse lemma using singularity theory can hold, yet the hypotheses of the Morse-Palais and Morse-Tromba lemmas fail. Another example shows how to… (More)

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